The carrier of the dust-associated photoluminescence process causing ERE in many dusty interstellar environments remains unidentified. Several competing models are more or less able to match the observed broad, unstructured ERE band. We now constrain the character of the ERE carrier further by determining the wavelengths of the radiation that initiates the ERE. Using the imaging capabilities of the HST, we have resolved the width of narrow ERE filaments appearing on the surfaces of externally illuminated molecular clouds in the bright reflection nebula NGC 7023 and compared them with the depth of penetration of radiation of known wavelengths into the same cloud surfaces. We identify photons with wavelengths shortward of 118 nm as the source of ERE initiation, not to be confused with ERE excitation, however. There are strong indications from the well-studied ERE in the Red Rectangle Nebula and in the high-|b| Galactic cirrus that the photon flux with wavelengths shortward of 118 nm is too small to actually excite the observed ERE, even with 100% quantum efficiency. We conclude, therefore, that ERE excitation results from a two-step process. The first, involving far-UV photons with E>10.5 eV, leads to the creation of the ERE carrier, most likely through photoionization or photodissociation of an existing precursor. The second, involving more abundant near-UV/optical photons, consists of the optical pumping of the previously created carrier, followed by subsequent deexcitation via photoluminescence. The latter process can occur many times for a single particle, depending upon the lifetime of the ERE carrier in its active state. While none of the previously proposed ERE models can match these new constraints, we note that under interstellar conditions most PAH molecules are ionized to the dication stage by photons with E>10.5 eV and that the electronic energy level structure of PAH dications is consistent with fluorescence in the wavelength band of the ERE. Therefore, PAH dications deserve further study as potential carriers of the ERE. Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. These observations are associated with program 9471.